Power electronics is an emerging technology. New power circuits are invented and have to be introduced into the power electronics curriculum. One of the interesting new circuits is the matrix converter (MC), and this paper analyses its working principles. A simple model is proposed to represent the power circuit, including the input filter. The power semiconductors are modelled as ideal bidirectional switches and the MC is controlled using a direct transfer function approach. The modulation strategy of the converter is explained in a complete and clear form. The commutation problem of two switches and the generation of overvoltages are clarified. The paper also includes a soft-switching commutation method that allows for a safe commutation of the switches. Finally a complete simulation scheme, using Matlab®-Simulink®, is discussed.